I, too, find it quite funny that you consider 2011 as "old" :D.
Of course this is not objectively wrong, since there is no absolute measure for this, but to somebody who played his first video games in the late 80s / early 90s and saw the gigantic changes that have happened since then, it's still an amusing statement :).
This opens up the interesting question how people of different ages perceive the development of games.
I, personally, and of course totally subjectively, make a very rough distinction between three eras of computer game history, from a mostly technological point of view:
First, there were the "dark ages", which to me means the time from the very first computer games (1960s? early 1970s?) until before I started playing video games myself. This was also roughly the time before the "IBM-compatible PC" (i.e. x86 running DOS and later Windows operating systems) became the dominating home computer standard around ca. 1992. Games from this time had very low-res graphics, very few (if any) colors, extremely simple animations and extremely crude sound (played by the built-in PC speaker, dedicated sound chips and external high-quality speakers didn't exist until very late in that era). Everything was still *way way* below of what is sold as "retro style" today (except for the pixel resolution maybe). I have personally played only very few specimen which I'd file under this category. Spontaneously, only the two very first computer games I ever played come to my mind: Tetris and Sokoban, both released in the mid-80s, in monochrome and later 4-color EGA (I think?) on my father's 80286 PC. Most others I know only from retro gaming magazines.
Then, roughly between 1992 and 2003, was the "early industrial age" of gaming. In that time, display resolutions, colors and sound slowly developed to more or less modern standards, the WWW and online gaming was born, and video games turned from a "nerd"/niche interest into a mainstream hobby. Also in that time, 3D graphics acceleration hardware was invented and became a standard component of every (gaming) PC. I personally perceive this era as the decade with the by far greatest changes and progress in video games (compare Wolfenstein 3D to Half-Life 2, or Dune 2 to Warcraft 3).
Finally, from 2003 until today, there is the "modern era". I define it by things like the introduction of programmable GPUs and shader APIs (DirectX 9 and newer), multi-core and 64-bit CPUs, online gaming becoming common and wide-spread, the advent of the 3D open world genre (e.g. GTA 3), by the introduction of Windows XP as the leading PC gaming OS (which was fundamentally new and different from former versions and is the architecture on which Windows 10 is still based more or less), and, again very subjectively, by the moment when game graphics finally becoming "good enough" for me. Younger people may see this with different eyes, but I perceive games like Half-Life 2 (from 2003) or especially Crysis (from 2007) by no means as "ugly" or definitively "old-tech", even though I do of course see the differences to newer titles. Roughly speaking, from the mid-2000s on, games reached a level of detail that finally allowed them to include all the details of a scene that you normally notice when you look around in an environment in real life without looking reeally closely (e.g. the individual elements of keyboards and CD-ROM drives of the computers in the science labs in Half-Life 2).
Now compare this to somebody who perceives games from 2011 als "old" :D.
As for The Binding of Isaac, what makes this game different from the typical highly commercialized "AAA" games is not the time in which it was made, but the people who made it and the target group they made it for. In 2011, very much the same graphically intensive multi-million-dollar productions as today have already existed, too, and they weren't even a new thing then. Battlefield 3, a perfect example, was released in 2011. While it looked somewhat less impressive as comparable games released this year, the overall concept and character was already exactly the same.
A final note though: To me, "classic" means something completely different from "old". I define "classic" as something that achieved an overall level of quality and/or uniqueness that makes it stand out greatly from other creations of its time and is thus "timeless". While it always takes some time for something to be recognized as a classic (which automatically rules out that it can be considered classic when it was just released), the label itself has nothing to do with age at all. By this definition, The Binding of Isaac is probably indeed a true classic (I haven't played it).